Advanced cryptographic method of multilayer diffusion in multidimension

ABSTRACT

The invention is related to working with variable diffusion functions on a multidimensional diffusion-area (plaintext/ciphertext); every diffusion function run in a cycle times, wherein repeating one certain times on the plaintext to get a ciphertext, and afterward, repeating the other times on the ciphertext to recover the plaintext, is performed in sequence to complete the encryption and the decryption. According to FIG.  1,  the system comprises of: inputting a plaintext in encryption or a ciphertext in decryption  100 ; reading every password segment in order, forward in encryption or backward in decryption  200 ; and further, converting the plaintext dimensions by the password segment  300;  implementing the diffusion function of Point  410,  Block  420  or Frame  430 , repeated T E  times in encryption, T D  times in decryption  400 ; going back to  200  until completing all password segments  500 , and outputting the ciphertext in encryption or the plaintext in decryption  600.

The application is a continuation in part of the prior USPTO patentapplication titled “A Cryptographic Method of Multilayer Diffusion inMultidimension” filed on Mar. 18, 2010, application Ser. No. 12/726,833,which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The invention is related to working with variable diffusion functions ona multidimensional diffusion-area (plaintext/ciphertext); everydiffusion function run in a cycle times, wherein repeating one certaintimes on the plaintext to get a ciphertext, afterward, repeating theother times on the ciphertext to recover the plaintext, is performed insequence to complete the encryption and the decryption. Through at leastone combination of point-diffusion, block-diffusion or frame-diffusion,the invention provides not only with a simpler multi-dimensioncalculation, but also with a higher security level.

BACKGROUND ART

The Applicant's following patent application is related to the inventionand is incorporated herein by reference: “A Cryptographic Method ofMultilayer Diffusion in Multidimension”, application Ser. No.12/726,833, filed Mar. 18, 2010.

In the prior art, such as DES (Data Encryption Standard) and AES(Advanced Encryption Standard), the password only works for repeatedlymixing the plaintext. On the contrary, being able to set off anydiffusion function, the password in the present invention may be takenas a crypto machine to randomly agitate the plaintext.

SUMMARY OF INVENTION

According to FIG. 1, the system comprises of: inputting a plaintext inencryption or a ciphertext in decryption 100; reading every passwordsegment in order, forward in encryption or backward in decryption 200;and further, converting the plaintext dimensions by the password segment300; implementing the diffusion function of Point 410, Block 420 orFrame 430, repeated T_(E) times in encryption, T_(D) times in decryption400; going back to 200 until completing all password segments 500, andoutputting the ciphertext in encryption or the plaintext in decryption600.

Notation of Point-Diffusion:

-   A: a n-dimension diffusion-area, wherein A is a d₁×₂× . . . ×d_(n)    binary matrix and includes a diffusion-center {dot over (P)} at the    coordinates (p₁, p₂, . . . p_(n)).-   S: a n-dimension medium, wherein S is a s₁×s₂× . . . ×s_(n) binary    matrix and includes an anchor-point {dot over (S)} at the    coordinates (s₁, s₂, . . . , s_(n)).-   AF({dot over (P)}): A performs the function of point-diffusion at    position {dot over (P)}, wherein S overlaps A by anchoring {dot over    (S)} to {dot over (P)}, and further,    AF({dot over (P)})=AF(p ₁ ,p ₂ , . . . , p _(n))=A⊕Ad _(1p) ⊕Ad    _(2p) ⊕ . . . ⊕Ad _(np) ⊕S;    Ad _(ip) =[A _(d) _(i) (2), . . . , A _(d) _(i) (p _(i)),A _(d) _(i)    (0),A _(d) _(i) (p _(i)), . . . , A _(d) _(i) (d _(i)−1)];-   AF(p₁, p₂ ^(t), . . . , p_(n)): A repeats to perform the function of    point-diffusion t times.-   T: a diffusion-cycle, wherein AF(p₁, p₂ ^(T), . . . , p_(n))=A,    letting T=2^(V+1), V=┌log₂ ν┐, ν=max(d₁, d₂, . . . , d_(n)).    Notation of Block-Diffusion:-   B: a n-dimension unit-block, wherein B is a u₁×u₂× . . . ×u_(n)    binary matrix and includes an anchor-point {dot over (B)} at the    coordinates (b₁, b₂, . . . ,b_(n)).-   ÂF({circumflex over (P)}): Â performs the function of    block-diffusion, wherein {dot over (B)} anchors to {dot over (P)}    and thus A is divided by B into Â with {circumflex over    (d)}₁×{circumflex over (d)}₂× . . . ×{circumflex over (d)}_(n) and    {dot over (P)} is arranged by B unit to {circumflex over (P)} at the    coordinates ({circumflex over (p)}₁, {circumflex over (p)}₂, . . .    {circumflex over (p)}_(n)), wherein {circumflex over    (d)}_(i)=┌(p_(i)−b)/u_(i)┐+┌(d_(i)−p_(i)+b_(i))/u_(i)┐ and    {circumflex over (p)}_(i)=┌(p_(i)−b_(i))/u_(i)┐+1, and further,    ÂF({circumflex over (p)} ₁ ,{circumflex over (p)} ₂ , . . . ,    {circumflex over (p)} _(n))=Â⊕{circumflex over ({circumflex over    (Ad)} _(1{circumflex over (p)}) ⊕{circumflex over ({circumflex over    (Ad)} _(2{circumflex over (p)}) ⊕ . . . ⊕{circumflex over    ({circumflex over (Ad)} _(n{circumflex over (p)}) ⊕S;    {circumflex over ({circumflex over (Ad)} _(i{circumflex over (p)})    =[Â _({circumflex over (d)}) _(i) (2), . . . , Â    _({circumflex over (d)}) _(i) ({circumflex over (p)} _(i)),Â    _({circumflex over (d)}) _(i) (0),Â _({circumflex over (d)}) _(i)    ({circumflex over (p)} _(i)), . . . , Â _({circumflex over (d)})    _(i) ({circumflex over (d)} _(i)−1)];-   ÂF({circumflex over (p)}₁,{circumflex over (p)}₂ ^(t), . . . ,    {circumflex over (p)}_(n)): Â repeats to perform the function of    block-diffusion t times.-   T: a diffusion-cycle, wherein ÂF({circumflex over (p)}₁, {circumflex    over (p)}₂ ^(T), . . . {circumflex over (p)}_(n))=A, letting    T=2^(V+1), V=┌log₂ ν┐, ν=max(┌d_(i)/b_(i)┐, 1≦i≦n).    Notation of Frame-Diffusion:-   F: a n-dimension frame, wherein F is a w₁×w₂× . . . ×w_(n) binary    matrix and includes an anchor-point {dot over (F)} at the    coordinates (f₁, f₂, . . . , f_(n)) and corner-points Ċ_(k) at the    coordinates (c_(k1), c_(k2), . . . , c_(kn)), where 1≦k≦2^(n).-   A    ({dot over (P)}): A performs the frame function of point-diffusion,    wherein F pastes to A by anchoring {dot over (F)} to {dot over (P)},    and further,

${{A{\overset{\Cap}{F}( \overset{.}{P} )}} = {{A{\overset{\Cap}{F}( {p_{1},p_{2},\ldots\mspace{14mu},p_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{{AF}( {\overset{.}{C}}_{k} )} \oplus {\sum\limits_{i = 1}^{n}\{ {A_{d_{i}}( p_{i} )} \}}}}}},$

-   -   wherein A is divided into 2^(n) diffusion subareas, in which        every subarea, every axis limited in (1˜p_(i)−1) or        (p_(i)+1˜d_(i)), is performed the point-diffusion AF(Ċ_(k)) at a        different position Ċ_(k)+{dot over (P)}−{dot over (F)}; and        further, every {A_(d) _(i) (p_(i))}=A_(d) _(i) (p_(i−1))⊕A_(d)        _(i) (p_(i))⊕A_(d) _(i) (p_(i+1)).

-   Â    ({circumflex over (P)}): Â performs the frame function of    block-diffusion, wherein F pastes to Â by anchoring {dot over (F)}    to {dot over (P)}, and further,

${{\hat{A}{\overset{\Cap}{F}( \hat{P} )}} = {{\hat{A}{\overset{\Cap}{F}( {{\hat{p}}_{1},{\hat{p}}_{2},\ldots\mspace{14mu},{\hat{p}}_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{\hat{A}{F( {\hat{C}}_{k} )}} \oplus {\sum\limits_{i = 1}^{n}\{ {{\hat{A}}_{{\hat{d}}_{i}}( {\hat{p}}_{i} )} \}}}}}},$

-   -   wherein Â is divided into 2^(n) diffusion subareas, in which        every subarea, every axis limited in (1˜{circumflex over        (p)}_(i)−1) or ({circumflex over (p)}_(i)+1˜{circumflex over        (d)}_(i)), is performed the block-diffusion ÂF(Ĉ_(k)) at a        different position Ĉ_(k)+{circumflex over (P)}−{circumflex over        (F)}, where ĉ_(i)=┌(c_(i)−b_(i))/u_(i)┐+1, {circumflex over        (f)}_(i)=┌(f_(i)−b_(i))/u_(i)┐+1, every        {Â_({circumflex over (d)}) _(i) ({circumflex over        (p)}_(i))}=Â_({circumflex over (d)}) _(i) ({circumflex over        (p)}_(i−1))⊕Â_({circumflex over (d)}) _(i) ({circumflex over        (p)}_(i))⊕Â_({circumflex over (d)}) _(i) ({circumflex over        (p)}_(i+1)).        Frame Function with Point-Diffusion:

According to FIG. 2, from FIG. 1, 430 combined with 410, the flow chartcomprises of: reading a diffusion-area A (plaintext/ciphertext) with adiffusion-center {dot over (P)}, a medium S with an anchor-point {dotover (S)}, and a frame F with an anchor-point {circumflex over (F)} and2^(n) corner-points Ĉ_(k) 201; anchoring the frame to thediffusion-center with its anchor-point 4311; implementing the framefunction of point-diffusion A

(p₁, p₂, . . . p_(n)) 4312; thus, further implementing thepoint-diffusions AF(c_(k1), c_(k2), . . . , c_(kn)), 1≦k≦2^(n), andA_(d) _(i) (p_(i)), 1≦i≦n 4313.

For an example as FIG. 4, A is a size of 8×8 with {dot over (P)} at (4,4), S is a size of 5×5 with {dot over (S)} at (1, 1), and F is a size of7×7 with {dot over (F)} at (4, 4) and Ċ₁ (1, 7), Ċ₂ at (7, 7), Ċ₃ at (7,1), Ċ₄ at (1, 1) 201; anchoring F to {dot over (P)} (4, 4) with {dotover (F)} (4, 4) 4311; correspondingly, pasting every Ċ_(k) to A andimplementing A

(4, 4) 4312; thus, further implementing AF(1, 7) , AF(7, 7) , AF(7, 1)and AF(1, 1) (may refer application Ser. No. 12/726,833, page 3-4.),{A_(x)(4)} and {A_(y)(4)} 4313, where calculations in detail are shownon FIG. 6.

Frame Function with Block-Diffusion:

According to FIG. 3, from FIG. 1, 430 combined with 420, the flow chartcomprises of: reading a diffusion-area A (plaintext/ciphertext) with adiffusion-center {dot over (P)}, a medium S with an anchor-point {dotover (S)}, a unit-block B with an anchor-point {dot over (B)}, and aframe F with an anchor-point {dot over (F)} and 2^(n) corner-pointsĊ_(k) 202; anchoring the frame and the unit-block to thediffusion-center with their own anchor-point 4321; arranging thediffusion-area and its diffusion-center by the unit-block 4322;implementing the frame function of block-diffusion Â

({circumflex over (p)}₁, {circumflex over (p)}₂, . . . {circumflex over(p)}_(n)) 4323; thus, further implementing the block-diffusionsÂF(ĉ_(k1), ĉ_(k2), . . . , ĉ_(kn)), 1≦k≦2^(n), andÂ_({circumflex over (d)}) _(i) ({circumflex over (p)}_(i)), 1≦i≦n 4324.

For an example as FIG. 5, A is a size of 8×8 with {dot over (P)} at (4,4), S is a size of 5×5 with {dot over (S)} at (1, 1), B is a size of 2×2with {circumflex over (B)} at (1, 1), and F is a size of 7×7 with {dotover (F)} at (4, 4) and Ċ₁ at (1, 7), Ċ₂ at (7, 7), Ċ₃ at (7, 1), Ċ₄ at(1, 1) 202; anchoring F to {dot over (P)} (4, 4) with {dot over (F)} (4,4), B to {dot over (P)} (4, 4) with {dot over (B)} (1, 1) 4321;correspondingly, arranging the 8×8 A to the 5×5 Â, the {dot over (P)}(4, 4) to the {circumflex over (P)} (3, 3) 4322; pasting every Ĉ_(k) toÂ and implementing Â

(3, 3) 4323; thus, further implementing ÂF(1, 4), ÂF(4, 4), ÂF(4, 1) andÂF(1, 1) (may refer application Ser. No. 12/726,833, page 7-8.),{Â_({circumflex over (x)})(3)} and {Â_(ŷ)(3)} 4324, where allcalculations in detail are shown on FIG. 7.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an exemplary flowchart in accordance with the presentinvention;

FIG. 2 is an exemplary detailed flowchart, frame diffusion of FIG. 1,adapted to run the frame function with point-diffusion;

FIG. 3 is an exemplary detailed flowchart, frame diffusion of FIG. 1,adapted to run the frame function with block-diffusion;

FIG. 4 is an exemplary block diagram in accordance with FIG. 2 adaptedfor two-dimensions;

FIG. 5 is an exemplary block diagram in accordance with FIG. 3 adaptedfor two-dimensions;

FIG. 6 is an exemplary detailed block diagram in accordance with FIG. 4;

FIG. 7 is an exemplary detailed block diagram in accordance with FIG. 5;

FIG. 8 is an exemplary block diagram in accordance with FIG. 2 adaptedfor three-dimensions.

DESCRIPTION OF EMBODYMENT

Suppose that a plaintext A equals “smoother”, in which the ASCII code is73 6d 6f 6f 74 68 65 72, stored in a 8×8 binary matrix as Table 1.

TABLE 1 ASCII 73 6d 6f 6f 74 68 65 72 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 01 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 0 0 0 0 0 0 0 0

Suppose that a password equals “Yourlips”, in which the ASCII code is 596f 75 72 6c 69 70 73. To clearly show the frame effect performed in theplaintext, the password firstly excludes the last digit 3, and secondlyforms into octal format to get 26 26 75.65 34 46 61 51 34 07, andthirdly adds 1 to each digit; the positions are shown in as Table 2.

TABLE 2 ASCII 26 26 75 65 34 46 61 51 34 07 Row 3 3 8 7 4 5 7 6 4 1Column 7 7 6 6 5 7 2 2 5 8

EXAMPLE 1 Frame Functions with Point-Diffusion

Supposes that a medium

${S = \begin{bmatrix}10011 \\01101 \\10111 \\10010 \\11101\end{bmatrix}},${dot over (S)}=(1,1); a frame F is a size of 7×7 with {dot over (F)} at(4, 4), and Ċ₁ at (1, 7), Ċ₂ at (7, 7), Ċ₃ at (7, 1), Ċ₄ at (1, 1).

In addition, reads every diffusion-center in order, if from 1 to 10 onencryption, then from 10 back to 1 on decryption; counts thediffusion-cycle T=2³⁺¹=16 times; and further, sets up if 1 time onencryption, then 15 times on decryption.

By math expressions, in encryption, inputs the plaintext A as A₀, runsthe encryption as A₀ ¹, A₁ ¹, . . . A₉ ¹ and obtains the output as A₁,A₂, . . . A₁₀, thus, to get a ciphertext A₁₀; reversely, in decryption,inputs the ciphertext A₁₀, runs the decryption as A₁₀ ¹⁵, A₉ ¹⁵, . . .A₁ ¹⁵ and obtains the output A₉, . . . , A₁, A₀, thus, to recover theplaintext A.

When {dot over (F)} anchors to every {dot over (P)}, by running a framefunction with point-diffusion every time, every Ċ_(k) is changedcorrespondingly; hereinafter,Ċ _(k) =Ċ _(k) +{dot over (P)}−{dot over (F)},and further,A _(k) ^(t+1) =A _(k) ^(t)

(p ₁ ,p ₂)=A _(k) ^(t) F(Ċ ₁)⊕A _(k) ^(t) F(Ċ ₂)⊕A _(k) ^(t) F(Ċ ₃)⊕A_(k) ^(t) F(Ċ ₄)⊕{A _(k) _(x) ^(t)(p ₁)}⊕{A _(k) _(y) ^(t)(p ₂)}.The details taken from password positions 1, 5 and 10 are shown asbelow:Encryption at the 1^(st) diffusion-center (3,7):

$\begin{matrix}{A_{0}^{1} = {{A{\overset{\Cap}{F}( {3,7} )}} = {{{AF}( {0,10} )} \oplus {{AF}( {6,10} )} \oplus}}} \\{{{AF}( {6,4} )} \oplus {{AF}( {0,4} )} \oplus \{ {A_{x}(3)} \} \oplus \{ {A_{y}(7)} \}} \\{= {\begin{bmatrix}0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{bmatrix} = {A_{1}.}}}\end{matrix}$Encryption at the 5^(th) diffusion-center (4,5):

$\begin{matrix}{A_{4}^{1} = {{A_{4}{\overset{\Cap}{F}( {4,5} )}} = {{A_{4}{F( {1,8} )}} \oplus {A_{4}{F( {7,8} )}} \oplus}}} \\{{A_{4}{F( {7,2} )}} \oplus {A_{4}{F( {1,2} )}} \oplus \{ {A_{4_{x}}(4)} \} \oplus \{ {A_{4_{y}}(5)} \}} \\{= {\begin{bmatrix}0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 \\0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\end{bmatrix} = {A_{5}.}}}\end{matrix}$

${{Encryption}\mspace{14mu}{at}\mspace{14mu}{the}\mspace{14mu} 10^{th}\mspace{14mu}{diffusion}\text{-}{{center}( {1,8} )}}:\begin{matrix}{A_{9}^{1} = {{A_{9}{\overset{︵}{F}( {1,8} )}} = {{A_{9}{F( {{- 2},11} )}} \oplus {A_{9}{F( {4,11} )}} \oplus {A_{9}{F( {4,5} )}} \oplus}}} \\{{A_{9}{F( {{- 2},5} )}} \oplus \{ {A_{9x}(1)} \} \oplus \{ {A_{9y}(8)} \}} \\{= {\begin{bmatrix}0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 \\1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 \\1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\1 & 0 & 1 & 1 & 1 & 0 & 1 & 0\end{bmatrix} = {A_{10}.}}}\end{matrix}$

${{Decryption}\mspace{14mu}{at}\mspace{14mu}{the}\mspace{14mu} 10^{th}\mspace{14mu}{diffusion}\text{-}{{center}( {1,8} )}}:\begin{matrix}{A_{10}^{15} = {{A_{10}^{14}{\overset{︵}{F}( {1,8} )}} = {{A_{10}^{14}{F( {{- 2},11} )}} \oplus {A_{10}^{14}{F( {4,11} )}} \oplus {A_{10}^{14}{F( {4,5} )}} \oplus}}} \\{{A_{10}^{14}{F( {{- 2},5} )}} \oplus \{ {A_{10x}^{14}(1)} \} \oplus \{ {A_{10y}^{14}(8)} \}} \\{= {\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\end{bmatrix} = {A_{9}.}}}\end{matrix}$Decryption at the 5^(th) diffusion-center (4,5):

$\begin{matrix}{A_{5}^{15} = {{A_{5}^{14}{\overset{\Cap}{F}( {4,5} )}} = {{A_{5}^{14}{F( {1,8} )}} \oplus {A_{5}^{14}{F( {7,8} )}} \oplus}}} \\{{A_{5}^{14}{F( {7,2} )}} \oplus {A_{5}^{14}{F( {1,2} )}} \oplus \{ {A_{5_{x}}^{14}(4)} \} \oplus \{ {A_{5_{y}}^{14}(5)} \}} \\{= {\begin{bmatrix}0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 \\0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 1 & 1 & 0\end{bmatrix} = {A_{4}.}}}\end{matrix}$Decryption at the 1^(st) diffusion-center (3,7):

$\begin{matrix}{A_{1}^{15} = {{A_{1}^{14}{\overset{\Cap}{F}( {3,7} )}} = {{A_{1}^{14}{F( {0,10} )}} \oplus {A_{1}^{14}{F( {6,10} )}} \oplus}}} \\{{A_{1}^{14}{F( {6,4} )}} \oplus {A_{1}^{14}{F( {0,4} )}} \oplus \{ {A_{1_{x}}^{14}(3)} \} \oplus \{ {A_{1_{y}}^{14}(7)} \}} \\{= {\begin{bmatrix}1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix} = {A.}}}\end{matrix}$

EXAMPLE 2 Frame Functions with Block-Diffusion

The Example 1 further joins with a unit-block B, wherein B is a size of2×2 with {dot over (B)} at (1, 1); thus, the frame F, arranged by B,with the anchor-point {circumflex over (F)} at (3, 3) and thecorner-points Ĉ₁ (1, 4), Ĉ₂ at (4, 4), Ĉ₃ at (4, 1), Ĉ₄ at (1, 1); readsevery diffusion-center in order, if from 1 to 10 on encryption, thenfrom 10 back to 1 on decryption; counts the diffusion-cycle T=2²⁺¹=8times (due to d_(i)/b_(i)=4=2²); and further, sets up if 1 time onencryption, then 7 times on decryption.

By math expressions, in encryption, inputs the plaintext A as A₀, runsthe encryption as Â₀ ¹, Â₁ ¹, . . . Â₉ ¹ and obtains the output as A₁,A₂, . . . A₁₀, thus, to get a ciphertext A₁₀; reversely, in decryption,inputs the ciphertext A₁₀, runs the decryption as Â₁₀ ⁷, Â₉ ⁷, . . . Â₁⁷ and obtains the output A₉, . . . , A₁, A₀, thus, to recover theplaintext A.

When {dot over (F)} and {dot over (B)} anchor to every {dot over (P)},by running a frame function with block-diffusion every time, every Ĉ_(k)is changed correspondingly; hereinafter,Ĉ _(k) =Ĉ _(k) +{circumflex over (P)}−{circumflex over (F)},and further,Â _(k) ^(t+1) =Â _(k) ^(t)

({circumflex over (p)} ₁ ,{circumflex over (p)} ₂)=Â _(k) ^(t) F(Ĉ ₁)⊕Â_(k) ^(t) F(Ĉ ₂)⊕Â _(k) ^(t) F(Ĉ ₃)⊕Â _(k) ^(t) F(Ĉ ₄)⊕{Â _(k)_({circumflex over (x)}) ^(t)({circumflex over (p)} ₁)}⊕{Â _(k) _(ŷ)^(t)({circumflex over (p)} ₂)}.The details taken from password positions 1, 5 and 10 are shown asbelow:Encryption at the 1^(st) diffusion-center (3,7):

$\begin{matrix}{{\hat{A}}_{0}^{1} = {{\hat{A}{\overset{\Cap}{F}( {2,4} )}} = {{\hat{A}{F( {0,5} )}} \oplus {\hat{A}{F( {3,5} )}} \oplus}}} \\{{\hat{A}{F( {3,2} )}} \oplus {\hat{A}{F( {0,2} )}} \oplus \{ {{\hat{A}}_{\hat{x}}(2)} \} \oplus \{ {{\hat{A}}_{\hat{y}}(4)} \}} \\{= {\begin{bmatrix}0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{bmatrix} = {A_{1}.}}}\end{matrix}$Encryption at the 5^(th) diffusion-center (4,5):

$\begin{matrix}{{\hat{A}}_{4}^{1} = {{{\hat{A}}_{4}{\overset{\Cap}{F}( {3,3} )}} = {{{\hat{A}}_{4}{F( {1,4} )}} \oplus {{\hat{A}}_{4}{F( {4,4} )}} \oplus}}} \\{{{\hat{A}}_{4}{F( {4,1} )}} \oplus {{\hat{A}}_{4}{F( {1,1} )}} \oplus \{ {{\hat{A}}_{4_{\hat{x}}}(3)} \} \oplus \{ {{\hat{A}}_{4_{\hat{y}}}(3)} \}} \\{= {\begin{bmatrix}0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 \\1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\end{bmatrix} = {A_{5}.}}}\end{matrix}$Encryption at the 10^(th) diffusion-center (1,8):

$\quad\begin{matrix}{{\hat{A}}_{9}^{1} = {{\hat{A}}_{9}{\overset{︵}{F}( {1,5} )}}} \\{= {{{\hat{A}}_{9}{F( {{- 1},6} )}} \oplus {{\hat{A}}_{9}{F( {2,6} )}} \oplus {{\hat{A}}_{9}{F( {2,3} )}} \oplus}} \\{{{\hat{A}}_{9}{F( {{- 1},3} )}} \oplus \{ {{\hat{A}}_{9\hat{x}}(1)} \} \oplus \{ {{\hat{A}}_{9\hat{y}}(5)} \}} \\{= \begin{bmatrix}0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{bmatrix}} \\{= {A_{10}.}}\end{matrix}$Decryption at the 10^(th) diffusion-center (1,8):

$\quad\begin{matrix}{{\hat{A}}_{10}^{7} = {{\hat{A}}_{10}^{6}{\overset{︵}{F}( {1,5} )}}} \\{= {{{\hat{A}}_{10}^{6}{F( {{- 1},6} )}} \oplus {{\hat{A}}_{10}^{6}{F( {2,6} )}} \oplus {{\hat{A}}_{10}^{6}{F( {2,3} )}} \oplus}} \\{{{\hat{A}}_{10}^{6}{F( {{- 1},3} )}} \oplus \{ {{\hat{A}}_{10\hat{x}}^{6}(1)} \} \oplus \{ {{\hat{A}}_{10\hat{y}}^{6}(5)} \}} \\{= \begin{bmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 \\0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{bmatrix}} \\{= {A_{9}.}}\end{matrix}$Decryption at the 5^(th) diffusion-center (4,5):

$\quad\begin{matrix}{{\hat{A}}_{5}^{7} = {{\hat{A}}_{5}^{6}{\overset{︵}{F}( {3,3} )}}} \\{= {{{\hat{A}}_{5}^{6}{F( {1,4} )}} \oplus {{\hat{A}}_{5}^{6}{F( {4,4} )}} \oplus {{\hat{A}}_{5}^{6}{F( {4,1} )}} \oplus}} \\{{{\hat{A}}_{5}^{6}{F( {1,1} )}} \oplus \{ {{\hat{A}}_{5\hat{x}}^{6}(3)} \} \oplus \{ {{\hat{A}}_{5\hat{y}}^{6}(3)} \}} \\{= \begin{bmatrix}0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 \\0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}} \\{= {A_{4}.}}\end{matrix}$Decryption at the 1^(st) diffusion-center (3,7):

$\quad\begin{matrix}{{\hat{A}}_{1}^{7} = {{\hat{A}}_{1}^{6}{\overset{︵}{F}( {2,4} )}}} \\{= {{{\hat{A}}_{1}^{6}{F( {0,5} )}} \oplus {{\hat{A}}_{1}^{6}{F( {3,5} )}} \oplus {{\hat{A}}_{1}^{6}{F( {3,2} )}} \oplus}} \\{{{\hat{A}}_{1}^{6}{F( {0,2} )}} \oplus \{ {{\hat{A}}_{1\hat{x}}^{6}(2)} \} \oplus \{ {{\hat{A}}_{1\hat{y}}^{6}(4)} \}} \\{= \begin{bmatrix}1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}} \\{= {A.}}\end{matrix}$

EXAMPLE 3 Frame Functions with Point-Diffusion and Block-Diffusion

The Example 2 further joins with a switch set Y=[1011011101]; readsevery diffusion-center and Y element in order, if from 1 to 10 onencryption, then from 10 back to 1 on decryption; counts thediffusion-cycle, if Y element is 1, then T=2³⁺¹=16 times for runningwith point-diffusions, otherwise, T=2²⁺¹=8 times for running withblock-diffusions, and further, sets up if 1 time on encryption, then 15or 7 times on decryption.

By math expressions, in encryption, inputs the plaintext A as A₀, runsthe encryption as A₀ ¹,Â₁ ¹,A₂ ¹,A₃ ¹,Â₄ ¹,A₅ ¹,A₆ ¹,A₇ ¹,Â₈ ¹,A₉ ¹ andobtains the output as A₁,A₂, . . . , A₉,A₁₀ thus, to get a ciphertextA₁₀; reversely, in decryption, inputs the ciphertext A₁₀, runs thedecryption as A₁₀ ¹⁵,Â₉ ⁷,A₈ ¹⁵,A₇ ¹⁵,A₆ ¹⁵,Â₅ ⁷,A₄ ¹⁵,A₃ ¹⁵,Â₂ ⁷,A₁ ¹⁵and obtains the output A₉,A₈, . . . , A₁,A₀, thus, to recover theplaintext A.

The details taken from password positions 1, 5 and 10 are shown asbelow:

Encryption at the 1^(st) diffusion-center (3,7): (Y(1)=1,point-diffusion)

$\quad\begin{matrix}{A_{0}^{1} = {A{\overset{︵}{F}( {3,7} )}}} \\{= {{{AF}( {0,10} )} \oplus {{AF}( {6,10} )} \oplus {{AF}( {6,4} )} \oplus}} \\{{{AF}( {0,4} )} \oplus \{ {A_{x}(3)} \} \oplus \{ {A_{y}(7)} \}} \\{= \begin{bmatrix}0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{bmatrix}} \\{= {A_{1}.}}\end{matrix}$Encryption at the 5^(th) diffusion-center (4,5): (Y(5)=0,block-diffusion)

$\begin{matrix}{{\hat{A}}_{4}^{1} = {{\hat{A}}_{4}{\overset{︵}{F}( {3,3} )}}} \\{= {{{\hat{A}}_{4}{F( {1,4} )}} \oplus {{\hat{A}}_{4}{F( {4,4} )}} \oplus {{\hat{A}}_{4}{F( {4,1} )}} \oplus}} \\{{{\hat{A}}_{4}{F( {1,1} )}} \oplus \{ {{\hat{A}}_{4\hat{x}}(3)} \} \oplus \{ {{\hat{A}}_{4\hat{y}}(3)} \}} \\{= \begin{bmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 \\0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 \\0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 1 & 1 & 0 & 1\end{bmatrix}} \\{= A_{5}}\end{matrix}$Encryption at the 10^(th) diffusion-center (1,8): (Y(10)=1,point-diffusion)

$\quad\begin{matrix}{A_{9}^{1\;} = {A_{9}{\overset{︵}{F}( {1,8} )}}} \\{= {{A_{9}{F( {{- 2},11} )}} \oplus {A_{9}{F( {4,11} )}} \oplus {A_{9}{F( {4,5} )}} \oplus}} \\{{A_{9}{F( {{- 2},5} )}} \oplus \{ {A_{9x}(1)} \} \oplus \{ {A_{9y}(8)} \}} \\{= \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 1 & 1 & 1 & 1\end{bmatrix}} \\{= A_{10}}\end{matrix}$Decryption at the 10^(th) diffusion-center (1,8): (Y(10)=1,point-diffusion)

$\quad\begin{matrix}{A_{10}^{15} = {A_{10}^{14}{\overset{︵}{F}( {1,8} )}}} \\{= {{A_{10}^{14}{F( {{- 2},11} )}} \oplus {A_{10}^{14}{F( {4,11} )}} \oplus {A_{10}^{14}{F( {4,5} )}} \oplus}} \\{{A_{10}^{14}{F( {{- 2},5} )}} \oplus \{ {A_{10x}^{14}(1)} \} \oplus \{ {A_{10y}^{14}(8)} \}} \\{= \begin{bmatrix}1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 \\0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 1\end{bmatrix}} \\{= {A_{9}.}}\end{matrix}$Decryption at the 5^(th) diffusion-center (4,5): (Y(5)=0,block-diffusion)

$\quad\begin{matrix}{{\hat{A}}_{5}^{7} = {{\hat{A}}_{5}^{6}{\overset{︵}{F}( {3,3} )}}} \\{= {{{\hat{A}}_{5}^{6}{F( {1,4} )}} \oplus {{\hat{A}}_{5}^{6}{F( {4,4} )}} \oplus {{\hat{A}}_{5}^{6}{F( {4,1} )}} \oplus}} \\{{{\hat{A}}_{5}^{6}{F( {1,1} )}} \oplus \{ {{\hat{A}}_{5\hat{x}}^{6}(3)} \} \oplus \{ {{\hat{A}}_{5\hat{y}}^{6}(3)} \}} \\{= \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{bmatrix}} \\{= A_{4}}\end{matrix}$Decryption at the 1^(st) diffusion-center (3,7): (Y(1)=1,point-diffusion)

$\quad\begin{matrix}{A_{1}^{15} = {A_{1}^{14}{\overset{︵}{F}( {3,7} )}}} \\{= {{A_{1}^{14}{F( {0,10} )}} \oplus {A_{1}^{14}{F( {6,10} )}} \oplus {A_{1}^{14}{F( {6,4} )}} \oplus}} \\{{A_{1}^{14}{F( {0,4} )}} \oplus \{ {A_{1x}^{14}(3)} \} \oplus \{ {A_{1y}^{14}(7)} \}} \\{= \begin{bmatrix}1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 \\1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}} \\{= {A.}}\end{matrix}$

From the examples, a two-dimension area is turned into 4 subareas byrunning a frame function; thus, according to FIG. 8, it is easy tounderstand that a three-dimension area is then turned into 8 subareasand every subarea, under three-dimensions, is performed apoint-diffusion or a block-diffusion (see more detail in applicationSer. No. 12/726,833, page 4-6, 9-11); by the same way, the invention iswell applied on a variable area of multi-dimensions.

In summation of the above description, the present invention hereincomplies with the constitutional, statutory, regulatory and treaty,patent application requirements and is herewith submitted for patentapplication. However, the description and its accompanied drawings areused for describing preferred embodiments of the present invention, andit is to be understood that the invention is not limited thereto. To thecontrary, it is intended to cover various modifications and similararrangements and procedures, and the scope of the appended claimstherefore should be accorded the broadest interpretation so as toencompass all such modifications and similar arrangements andprocedures.

What is claimed is:
 1. A computer-implemented cryptographic methodcomprising a plaintext M run by at least one variable module stored in amemory to perform the following steps by a processor: selecting an-dimension diffusion-area A, wherein A is a d₁×d₂× . . . ×d_(n) binarymatrix and includes a diffusion-center {dot over (P)} at the coordinates(p₁, p₂, . . . p_(n)); selecting a frame function of point-diffusion A

({dot over (P)}), wherein${{A{\overset{︵}{F}( \overset{.}{P} )}} = {{A{\overset{︵}{F}( {p_{1},p_{2},\ldots\mspace{14mu},p_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{{AF}( {\overset{.}{C}}_{k} )} \oplus {\sum\limits_{i = 1}^{n}\{ {A_{d_{i}}( p_{i} )} \}}}}}};$setting a diffusion-cycle T, wherein T=2^(V−1), V=┌log₂ ν┐, andν=max(d₁, d₂, . . . , d_(n)); letting T=T_(E)+T_(D), and the methodfurther comprising steps of: (a) encrypting M, wherein lets A=M and aciphertext C=A{circumflex over (F)}(p₁,p₂ _(T) ^(E), . . . , p_(n)); and(b) decrypting C, wherein lets A=C and the plaintext M=A{circumflex over(F)}(p₁, p₂ _(T) ^(D), . . . , p_(n)); wherein the said encrypting anddecrypting steps are run by the said computer-processor.
 2. Acomputer-implemented cryptographic method comprising a plaintext M runby at least one variable module stored in a memory to perform thefollowing steps by a processor: selecting a n-dimension diffusion-areaA, wherein A is a d₁×d₂× . . . ×d_(n) binary matrix and includes adiffusion-center {dot over (P)} at the coordinates (p₁, p₂, . . .p_(n)); selecting a n-dimension unit-block B, wherein B is a u₁×u₂× . .. ×u_(n) binary matrix and includes an anchor-point {dot over (B)} atthe coordinates (b₁, b₂, . . . , b_(n)); letting {dot over (B)} anchorsto {dot over (P)}, wherein A is divided by B into Â with {circumflexover (d)}₁×{circumflex over (d)}₂× . . . ×{circumflex over (d)}_(n) and{dot over (P)} is arranged by B unit to {circumflex over (P)} at thecoordinates ({circumflex over (p)}₁, {circumflex over (p)}₂, . . .{circumflex over (p)}_(n)), wherein {circumflex over(p)}_(i)=┌(p_(i)−b_(i))/u_(i)┐+1 and {circumflex over(d)}_(i)=┌(p_(i)−b_(i))/u_(i)┐+┌(d_(i)−p_(i)+b_(i))/u_(i)┐; selecting aframe function of block-diffusion Â

({circumflex over (P)}), wherein${{\hat{A}{\overset{︵}{F}( \hat{P} )}} = {{\hat{A}{\overset{︵}{F}( {{\hat{p}}_{1},{\hat{p}}_{2},\ldots\mspace{14mu},{\hat{p}}_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{\hat{A}{F( {\hat{C}}_{k} )}} \oplus {\sum\limits_{i = 1}^{n}\{ {{\hat{A}}_{{\hat{d}}_{i}}( {\hat{p}}_{i} )} \}}}}}};$setting a diffusion-cycle T, wherein T=2^(V+1), V=┌log₂ ν┐, andν=max(┌d_(i)/b_(i)┐, 1≦i≦n); letting T=T_(E)+T_(D), and the methodfurther comprising steps of: (a) encrypting M, wherein lets Â=M and aciphertext C=Â{circumflex over (F)}({circumflex over (p)}₁, {circumflexover (p)}₂ _(T) ^(E), . . . , {circumflex over (p)}_(n)); and (b)decrypting C, wherein lets Â=C and the plaintext M=Â{circumflex over(F)}({circumflex over (p)}×₁, {circumflex over (p)}₂ _(T) ^(D), . . . ,{circumflex over (p)}_(n)); wherein the said encrypting and decryptingsteps are run by the said computer-processor.
 3. A computer-implementedcryptographic method comprising a plaintext M run by at least onevariable module stored in a memory to perform the following steps by aprocessor: selecting a n-dimension diffusion-area A, wherein A is ad₁×d₂× . . . ×d_(n) binary matrix and includes a diffusion-center {dotover (P)} at the coordinates (p₁, p₂, . . . p_(n)); selecting a framefunction of point-diffusion A

({dot over (P)}), wherein${{A{\overset{︵}{F}( \overset{.}{P} )}} = {{A{\overset{︵}{F}( {p_{1},p_{2},\ldots\mspace{14mu},p_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{{AF}( {\overset{.}{C}}_{k} )} \oplus {\sum\limits_{i = 1}^{n}\{ {A_{d_{i}}( p_{i} )} \}}}}}};$selecting a n-dimension unit-block B, wherein B is a u₁×u₂× . . . ×u_(n)binary matrix and includes an anchor-point {dot over (B)} at thecoordinates (b₁, b₂, . . . , b_(n)); letting {dot over (B)} anchors to{dot over (P)}, wherein A is divided by B into Â with {circumflex over(d)}₁×{circumflex over (d)}₂× . . . {circumflex over (d)}_(n) and {dotover (P)} is arranged by B unit to {circumflex over (P)} at thecoordinates ({circumflex over (p)}₁, {circumflex over (p)}₂, . . .{circumflex over (p)}_(n)), wherein {circumflex over(p)}_(i)=┌(p_(i)−b_(i))/u_(i)┐+1 and {circumflex over(d)}_(i)=┌(p_(i)−b_(i))/u_(i)┐+┌(d_(i)−p_(i)+b_(i))/u_(i)┐; selecting aframe function of block-diffusion Â

({circumflex over (P)}), wherein${{\hat{A}{\overset{︵}{F}( \hat{P} )}} = {{\hat{A}{\overset{︵}{F}( {{\hat{p}}_{1},{\hat{p}}_{2},\ldots\mspace{14mu},{\hat{p}}_{n}} )}} = {\sum\limits_{k = 1}^{2^{n}}{{\hat{A}{F( {\hat{C}}_{k} )}} \oplus {\sum\limits_{i = 1}^{n}\{ {{\hat{A}}_{{\hat{d}}_{i}}( {\hat{p}}_{i} )} \}}}}}};$selecting a switch Y, wherein Y represents for running A

({dot over (P)}) with a first value, Â

({circumflex over (P)}) with a second value; setting a diffusion-cycleT₁, wherein T₁=2^(V+1), V=┌log₂ ν┐, and ν=max(d₁, d₂, . . . , d_(n));setting a diffusion-cycle T₂, wherein T₂=2^(V+1), V=┌log₂ ν┐, andν=max(┌d_(i)/b_(i)┐, 1≦i≦n); and the method further comprising steps of: (a) encrypting M, wherein if Y equals said first value, lettingT₁=T_(E1)+T_(D1) and A=M ,then a ciphertext C=A{circumflex over (F)}(p₁,p₂ _(T) ^(E1), . . . , p_(n)):if Y equals said second value, lettingT₂=T_(E2)+T_(D2) and Â=M, then C=Â{circumflex over (F)}({circumflex over(p)}₁,{circumflex over (p)}₂ _(T) ^(E1), . . . , {circumflex over(p)}_(n)); and (b) decrypting C, wherein if Y equals said first value,letting A=C, then the plaintext M=A{circumflex over (F)}(p₁,p₂ _(T)^(D1), . . . , p_(n)): if Y equals said second value, letting Â=C, thenM=Â{circumflex over (F)}({circumflex over (p)}₁,{circumflex over (p)}₂_(T) ^(D1), . . . , {circumflex over (p)}_(n)); wherein the saidencrypting and decrypting steps are run by the said computer-processor.